Nonlinear evolution of a three-dimensional transverse wave packet in a hot plasma including the effect of its interaction with an ion-acoustic wave

Abstract

By a perturbation method two coupled nonlinear partial differential equations are obtained for the nonlinear evolution of a three dimensional transverse wave packet in a hot plasma including the effect of its interaction with a long wavelength ion-acoustic wave. From these two equations a nonlinear dispersion relation is obtained, from which the instability condition of a uniform transverse wave train including the effect of its interaction, both at resonance and at nonresonance with a long wavelength ion-acoustic wave, are deduced. Resonance occurs when the component of group velocity of the longitudinal wave along the direction of propagation of the ion-acoustic wave is equal to the phase velocity of the wave. Assuming the usual type of dependence of amplitude on space and time the coupled equations are transformed into two other coupled equations, which reduced to a single nonliear Schrödingsr equation when three dimensionality is disregarded. It is found that these three transformed equations cannot give instability condition at resonance.